What is the relationship between gravitational potential and gravitational field strength?
Practice Questions
1 question
Q1
What is the relationship between gravitational potential and gravitational field strength?
V = -g * r
g = -dV/dr
V = g * r
g = dV/dr
The gravitational field strength g is the negative gradient of the gravitational potential V, given by g = -dV/dr.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the relationship between gravitational potential and gravitational field strength?
Solution: The gravitational field strength g is the negative gradient of the gravitational potential V, given by g = -dV/dr.
Steps: 6
Step 1: Understand that gravitational potential (V) is a measure of the potential energy per unit mass at a point in a gravitational field.
Step 2: Recognize that gravitational field strength (g) is the force experienced by a unit mass in that field.
Step 3: Learn that the relationship between gravitational potential and gravitational field strength is based on how potential changes with distance.
Step 4: The term 'gradient' refers to how steeply something changes. In this case, it means how quickly gravitational potential changes as you move away from a mass.
Step 5: The formula g = -dV/dr shows that gravitational field strength (g) is equal to the negative change in gravitational potential (dV) with respect to distance (dr).
Step 6: The negative sign indicates that as you move away from a mass, the gravitational potential decreases, while the gravitational field strength points towards the mass.
